Question

1. (7pt) The Scholastic Aptitude Test (SAT) contains three sections: critical reading, mathematics and writing. Each part is scored on a 500-point scale. Information on test scores for the 2018 version of SAT is available at the College Board website. A sample of SAT scores for 5 students follow:

                                                                                                                       ANOVA Table

Source of variation	Sum of Squares (SS)	Degrees of freedom	Mean Square (MS)	F
Treatment	93.3	2.0	46.67	8.75
Error	64.0	12.0	5.33
Total	157.3	14

                 SAT scores - 2017

                                                   

Student	Reading	Math	Writing
1	453	458	465
2	456	458	459
3	454	460	457
4	458	455	461
5	454	454	463
mean	455	457	461

1. (5pt) Conduct a Fisher’s LSD test allowing for 5% error.

2. (2pt) The level of difficulty for all the three sections of the SAT, measured by the score, are supposed to be the same. Do you agree with this after the results of the LSD test? WHY?

Answer 1

Solution:

Given that , = 455,

= 457

= 461

Alpha = 0.05,

df error = 12 and MS error = 5.33
na = nb = 5

The value for Alpha = 0.05, df = 12 is 2.1788

LSD = t critical sqrt(MSE (1/na + 1*/nb) = 2.1788 sqrt[5.33 (1/5 + 1/5)]
LSD = 3.18

If the absolute value difference of Means (taking 2 at a time ABS(Mi - Mj) is \geq LSD, then reject the hypothesis that the means are the same.

No, we cannot agree with the results that the mean are the same, because after conducting Fishers LSD, we see that there is a significant difference between Mean 1 and Mean3 and between Mean2 and Mean 3.